You can say, "The shop is re-opened!" That is using "re-opened" as an adjective.
I think a native speaker would be more likely to use "re-open" as a verb in a sentence like this, and say, "The shop was re-opened." Note that if it is open now, it must have been re-opened at some time in the past, so you must use the past tense. If it is presently in the process of opening again, you can say, "The shop is re-opening".
You can't say "the shop is re-open". That's just wrong. "Re-open" is not an adjective, and it is the wrong tense to use as a verb here.
By the way, you could also say, "The shop is open again".